/*
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
   SLEPc - Scalable Library for Eigenvalue Problem Computations
   Copyright (c) 2002-2021, Universitat Politecnica de Valencia, Spain

   This file is part of SLEPc.
   SLEPc is distributed under a 2-clause BSD license (see LICENSE).
   - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
*/

static char help[] = "Simple quadratic eigenvalue problem.\n\n"
  "The command line options are:\n"
  "  -n <n>, where <n> = number of grid subdivisions in x dimension.\n"
  "  -m <m>, where <m> = number of grid subdivisions in y dimension.\n\n";

#include <slepcpep.h>

int main(int argc,char **argv)
{
  Mat            M,C,K,A[3];      /* problem matrices */
  PEP            pep;             /* polynomial eigenproblem solver context */
  PetscInt       N,n=10,m,Istart,Iend,II,nev,i,j,nconv;
  PetscBool      flag,terse;
  PetscReal      error,re,im;
  PetscScalar    kr,ki;
  Vec            xr,xi;
  BV             V;
  PetscRandom    rand;
  PetscErrorCode ierr;

  ierr = SlepcInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr;

  ierr = PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsGetInt(NULL,NULL,"-m",&m,&flag);CHKERRQ(ierr);
  if (!flag) m=n;
  N = n*m;
  ierr = PetscPrintf(PETSC_COMM_WORLD,"\nQuadratic Eigenproblem, N=%" PetscInt_FMT " (%" PetscInt_FMT "x%" PetscInt_FMT " grid)\n\n",N,n,m);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
     Compute the matrices that define the eigensystem, (k^2*M+k*C+K)x=0
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /* K is the 2-D Laplacian */
  ierr = MatCreate(PETSC_COMM_WORLD,&K);CHKERRQ(ierr);
  ierr = MatSetSizes(K,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
  ierr = MatSetFromOptions(K);CHKERRQ(ierr);
  ierr = MatSetUp(K);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(K,&Istart,&Iend);CHKERRQ(ierr);
  for (II=Istart;II<Iend;II++) {
    i = II/n; j = II-i*n;
    if (i>0) { ierr = MatSetValue(K,II,II-n,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
    if (i<m-1) { ierr = MatSetValue(K,II,II+n,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
    if (j>0) { ierr = MatSetValue(K,II,II-1,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
    if (j<n-1) { ierr = MatSetValue(K,II,II+1,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
    ierr = MatSetValue(K,II,II,4.0,INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(K,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /* C is the 1-D Laplacian on horizontal lines */
  ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
  ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
  ierr = MatSetFromOptions(C);CHKERRQ(ierr);
  ierr = MatSetUp(C);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(C,&Istart,&Iend);CHKERRQ(ierr);
  for (II=Istart;II<Iend;II++) {
    i = II/n; j = II-i*n;
    if (j>0) { ierr = MatSetValue(C,II,II-1,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
    if (j<n-1) { ierr = MatSetValue(C,II,II+1,-1.0,INSERT_VALUES);CHKERRQ(ierr); }
    ierr = MatSetValue(C,II,II,2.0,INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /* M is a diagonal matrix */
  ierr = MatCreate(PETSC_COMM_WORLD,&M);CHKERRQ(ierr);
  ierr = MatSetSizes(M,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
  ierr = MatSetFromOptions(M);CHKERRQ(ierr);
  ierr = MatSetUp(M);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(M,&Istart,&Iend);CHKERRQ(ierr);
  for (II=Istart;II<Iend;II++) {
    ierr = MatSetValue(M,II,II,(PetscReal)(II+1),INSERT_VALUES);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(M,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                Create the eigensolver and set various options
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /*
     Create eigensolver context
  */
  ierr = PEPCreate(PETSC_COMM_WORLD,&pep);CHKERRQ(ierr);

  /*
     Set matrices and problem type
  */
  A[0] = K; A[1] = C; A[2] = M;
  ierr = PEPSetOperators(pep,3,A);CHKERRQ(ierr);
  ierr = PEPSetProblemType(pep,PEP_HERMITIAN);CHKERRQ(ierr);

  /*
     In complex scalars, use a real initial vector since in this example
     the matrices are all real, then all vectors generated by the solver
     will have a zero imaginary part. This is not really necessary.
  */
  ierr = PEPGetBV(pep,&V);CHKERRQ(ierr);
  ierr = BVGetRandomContext(V,&rand);CHKERRQ(ierr);
  ierr = PetscRandomSetInterval(rand,-1,1);CHKERRQ(ierr);

  /*
     Set solver parameters at runtime
  */
  ierr = PEPSetFromOptions(pep);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                      Solve the eigensystem
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = PEPSolve(pep);CHKERRQ(ierr);

  /*
     Optional: Get some information from the solver and display it
  */
  ierr = PEPGetDimensions(pep,&nev,NULL,NULL);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD," Number of requested eigenvalues: %" PetscInt_FMT "\n",nev);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
                    Display solution and clean up
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /* show detailed info unless -terse option is given by user */
  ierr = PetscOptionsHasName(NULL,NULL,"-terse",&terse);CHKERRQ(ierr);
  if (terse) {
    ierr = PEPErrorView(pep,PEP_ERROR_BACKWARD,NULL);CHKERRQ(ierr);
  } else {
    ierr = PEPGetConverged(pep,&nconv);CHKERRQ(ierr);
    if (nconv>0) {
      ierr = MatCreateVecs(M,&xr,&xi);CHKERRQ(ierr);
      /* display eigenvalues and relative errors */
      ierr = PetscPrintf(PETSC_COMM_WORLD,
           "\n           k          ||P(k)x||/||kx||\n"
           "   ----------------- ------------------\n");CHKERRQ(ierr);
      for (i=0;i<nconv;i++) {
        /* get converged eigenpairs */
        ierr = PEPGetEigenpair(pep,i,&kr,&ki,xr,xi);CHKERRQ(ierr);
        /* compute the relative error associated to each eigenpair */
        ierr = PEPComputeError(pep,i,PEP_ERROR_BACKWARD,&error);CHKERRQ(ierr);
#if defined(PETSC_USE_COMPLEX)
        re = PetscRealPart(kr);
        im = PetscImaginaryPart(kr);
#else
        re = kr;
        im = ki;
#endif
        if (im!=0.0) {
          ierr = PetscPrintf(PETSC_COMM_WORLD," %9f%+9fi   %12g\n",(double)re,(double)im,(double)error);CHKERRQ(ierr);
        } else {
          ierr = PetscPrintf(PETSC_COMM_WORLD,"   %12f       %12g\n",(double)re,(double)error);CHKERRQ(ierr);
        }
      }
      ierr = PetscPrintf(PETSC_COMM_WORLD,"\n");CHKERRQ(ierr);
      ierr = VecDestroy(&xr);CHKERRQ(ierr);
      ierr = VecDestroy(&xi);CHKERRQ(ierr);
    }
  }
  ierr = PEPDestroy(&pep);CHKERRQ(ierr);
  ierr = MatDestroy(&M);CHKERRQ(ierr);
  ierr = MatDestroy(&C);CHKERRQ(ierr);
  ierr = MatDestroy(&K);CHKERRQ(ierr);
  ierr = SlepcFinalize();
  return ierr;
}

/*TEST

   testset:
      args: -pep_nev 4 -pep_ncv 21 -n 12 -terse
      output_file: output/ex16_1.out
      test:
         suffix: 1
         args: -pep_type {{toar qarnoldi}}
      test:
         suffix: 1_linear
         args: -pep_type linear -pep_linear_explicitmatrix
         requires: !single
      test:
         suffix: 1_linear_symm
         args: -pep_type linear -pep_linear_explicitmatrix -pep_linear_eps_gen_indefinite -pep_scale scalar -pep_linear_bv_definite_tol 1e-12
         requires: !single
      test:
         suffix: 1_stoar
         args: -pep_type stoar -pep_scale scalar
         requires: double !cuda
      test:
         suffix: 1_stoar_t
         args: -pep_type stoar -pep_scale scalar -st_transform
         requires: double !cuda

TEST*/
